An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 29

Schips Department Store operates a fleet of 10 trucks. The trucks arrive at random times throughout the day at the store's truck dock to be loaded with new deliveries or to have incoming shipments from the regional warehouse unloaded. Each truck returns to the truck hour. The service rate is 4 trucks per hour. Using the Poisson arrivals and exponential service times model with a finite calling population of trucks, determine the following operating characteristics:
a. The probability no trucks are at the truck dock
b. The average number of trucks waiting for loading/unloading
c. The average number of trucks in the truck dock area
d. The average waiting time before loading/unloading begins
e. The average waiting time in the system
f. What is the hourly cost of operation if the cost is $50 per hour for each truck and $30 per hour for the truck dock?
g. Consider a two-channel truck dock operation where the second channel could be operated for an additional $30 per hour. How much would the average number of trucks waiting for loading/unloading have to be reduced to make the two-channel truck dock economically feasible?
h. Should the company consider expanding to the two-channel truck dock? Explain.